Finite Group Databasebeta

← #154011

Subgroups — #154011

Order 512.

2954 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1444C211yesmaximal, characteristic
2C2×#1436C212yesmaximal
3C2×#1436C212yesmaximal
4C2×C4⋊#95C212yesmaximal
5#7557C212yesmaximal
6#7557C212yesmaximal
7#7556C211yesmaximal, characteristic
8#7554C211yesmaximal, characteristic
9#7554C212yesmaximal
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2212yes—
13C23×C42C2211yescharacteristic
14C23×C42C2212yes—
15C22×#95C2212yes—
16C22×#95C2212yes—
17C22×#95C2212yes—
18C22×#95C2211yescharacteristic
19C22×#95C2212yes—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2211yescharacteristic
26C22×#95C2211yescharacteristic
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2211yescharacteristic
30C22×#95C2211yescharacteristic
31#1444C418yescomplemented
32#1436—28no—
33#1436C4116yescomplemented
34C4⋊#95—28no—
35C24×C4C2311yescharacteristic
36C24×C4C2312yes—
37C24×C4C2312yes—
38C24×C4C2311yescharacteristic
39C24×C4C2312yes—
40C24×C4C2312yes—
41C24×C4C2311yescharacteristic
42C24×C4C2312yes—
43C24×C4C2312yes—
44C22×C4⋊C4—24no—
45C22×C4⋊C4—24no—
46C22×C4⋊C4—42no—
47C22×C4⋊C4—42no—
48C22×C4⋊C4—42no—
49C22×C4⋊C4—42no—
50C22×C4⋊C4—42no—
51C22×C4⋊C4—42no—
52C22×C4⋊C4—42no—
53C22×C4⋊C4—42no—
54C22×C4⋊C4—42no—
55C22×C4⋊C4—42no—
56C22×C4⋊C4—41no—
57C22×C4⋊C4—41no—
58C22×C4⋊C4C2×C418yes—
59C22×C4⋊C4C2×C414yes—
60C22×C4⋊C4C2×C418yes—
61C22×C4⋊C4D418yes—
62C22×C4⋊C4Q818yes—
63C22×C42—24no—
64C22×C42—24no—
65C22×C42—24no—
66C22×C42—22no—
67C22×C42—42no—
68C22×C42—42no—
69C22×C42—42no—
70C22×C42—42no—
71C22×C42—42no—
72C22×C42—41no—
73C22×C42—41no—
74C22×C42C2×C418yes—
75C2×#95—24no—
76C2×#95—24no—
77C2×#95—24no—
78C2×#95—24no—
79C2×#95—24no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—24no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—42no—
93C2×#95—42no—
94C2×#95—41no—
95C2×#95—42no—
96C2×#95—41no—
97C2×#95—42no—
98C2×#95—41no—
99C2×#95—41no—
100C2×#95—42no—
101C2×#95—41no—
102C2×#95—42no—
103C2×#95—42no—
104C2×#95—42no—
105C2×#95—42no—
106C2×#95—42no—
107C2×#95—42no—
108C2×#95—42no—
109C2×#95—42no—
110C2×#95—41no—
111C2×#95C2×C418yes—
112C2×#95C2×C418yes—
113C2×#95C2×C418yes—
114C2×#95C2×C418yes—
115C2×#95C2×C418yes—
116C2×#95C2×C414yes—
117C2×#95C2×C418yes—
118C2×#95C2×C414yes—
119C2×#95Q814yes—
120C25C2411yescharacteristic
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—21no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—21no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—21no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—21no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—21no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4C22×C414yes—
217C23×C4C22×C412yes—
218C23×C4C22×C414yes—
219C23×C4C22×C412yes—
220C23×C4C22×C414yes—
221C23×C4C22×C414yes—
222C23×C4C22×C414yes—
223C23×C4C22×C412yes—
224C23×C4C22×C414yes—
225C23×C4C22×C414yes—
226C23×C4C22×C414yes—
227C23×C4C22×C414yes—
228C23×C4C2×D414yes—
229C23×C4C2×D414yes—
230C23×C4C2×D414yes—
231C23×C4C2×Q814yes—
232C23×C4C2×Q814yes—
233C23×C4C2×Q812yes—
234C23×C4C2×Q814yes—
235C23×C4C2×Q814yes—
236C23×C4#4114yes—
237C23×C4#4112yes—
238C23×C4#4114yes—
239C23×C4#4114yes—
240C2×C4⋊C4—216no—
241C2×C4⋊C4—48no—
242C2×C4⋊C4—48no—
243C2×C4⋊C4—48no—
244C2×C4⋊C4—48no—
245C2×C4⋊C4—44no—
246C2×C4⋊C4—48no—
247C2×C4⋊C4—48no—
248C2×C4⋊C4—48no—
249C2×C4⋊C4—48no—
250C2×C4⋊C4—48no—
251C2×C4⋊C4—48no—
252C2×C4⋊C4—48no—
253C2×C4⋊C4—48no—
254C2×C4⋊C4—48no—
255C2×C4⋊C4—44no—
256C2×C4⋊C4—48no—
257C2×C4⋊C4—44no—
258C2×C4⋊C4C4⋊C4132yescomplemented
259C2×C42—216no—
260C2×C42—48no—
261C2×C42—48no—
262C2×C42—44no—
263C2×C42—48no—
264C2×C42—48no—
265C2×C42—48no—
266C2×C42—48no—
267C2×C42—48no—
268C2×C42—48no—
269C2×C42—44no—
270C2×C42—44no—
271#95—216no—
272#95—216no—
273#95—216no—
274#95—48no—
275#95—48no—
276#95—44no—
277#95—44no—
278#95—44no—
279#95—48no—
280#95—48no—
281#95—48no—
282#95—48no—
283#95—48no—
284#95—48no—
285#95—44no—
286#95C42116yescomplemented
287C24C23×C412yes—
288C24C23×C411yescharacteristic
289C24C22×D412yes—
290C24C22×Q812yes—
291C24C22×Q811yescharacteristic
292C24C2×#4112yes—
293C24C2×#4112yes—
294C24C2×#4112yes—
295C24C2×#4111yescharacteristic
296C24H(5,𝔽2)11yescharacteristic
297C24H(5,𝔽2)12yes—
298C24H(5,𝔽2)12yes—
299C24H(5,𝔽2)12yes—
300C24H(5,𝔽2)12yes—
301C24H(5,𝔽2)11yescharacteristic
302C24H(5,𝔽2)11yescharacteristic
303C242−1+412yes—
304C242−1+411yescharacteristic
305C242−1+412yes—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—41no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—41no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—41no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—41no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4C2×C4214yes—
570C22×C4C2×C4218yes—
571C22×C4C2×C4⋊C418yes—
572C22×C4C2×C4⋊C418yes—
573C22×C4C2×C4⋊C418yes—
574C22×C4#11718yes—
575C22×C4C4×D418yes—
576C22×C4C4×D418yes—
577C22×C4C4×Q818yes—
578C22×C4C4×Q814yes—
579C22×C4C4×Q818yes—
580C22×C4C4×Q818yes—
581C4⋊C4—432no—
582C4⋊C4—432no—
583C4⋊C4—416no—
584C42—432no—
585C42—416no—
586C23C22×C4211yescharacteristic
587C23C22×C4⋊C412yes—
588C23C2×#11712yes—
589C23C2×C4×D412yes—
590C23C2×C4×D412yes—
591C23C2×C4×Q812yes—
592C23C2×C4×Q812yes—
593C23C2×C4×Q812yes—
594C23C2×C4×Q811yescharacteristic
595C23C4×#4111yescharacteristic
596C23C4×#4112yes—
597C23#51812yes—
598C23#51812yes—
599C23#51811yescharacteristic
600C23#51812yes—
601C23#51812yes—
602C23#51811yescharacteristic
603C23#51911yescharacteristic
604C23#52012yes—
605C23#52012yes—
606C23#52011yescharacteristic
607C23#52012yes—
608C23#52012yes—
609C23#52012yes—
610C23#52012yes—
611C23#53412yes—
612C23#53412yes—
613C23#53512yes—
614C23#53612yes—
615C23#53812yes—
616C23#53812yes—
617C23#53812yes—
618C23#53812yes—
619C23#53812yes—
620C23#53811yescharacteristic
621C23#53912yes—
622C23#53912yes—
623C23#53912yes—
624C23#53912yes—
625C23#53911yescharacteristic
626C23#53912yes—
627C23#54012yes—
628C23#54112yes—
629C23#54212yes—
630C23#54312yes—
631C23#54312yes—
632C23#54311yescharacteristic
633C23#54412yes—
634C23#54412yes—
635C23#54411yescharacteristic
636C23#54412yes—
637C23D4211yescharacteristic
638C23#54612yes—
639C23#54612yes—
640C23#54712yes—
641C23D4×Q812yes—
642C23D4×Q812yes—
643C23#55012yes—
644C23#55012yes—
645C23#55212yes—
646C23#55212yes—
647C23#55312yes—
648C23#55312yes—
649C23#55412yes—
650C23#55412yes—
651C23#55412yes—
652C23#55412yes—
653C23#55412yes—
654C23#55512yes—
655C23#55512yes—
656C23#55511yescharacteristic
657C23#55612yes—
658C23#55712yes—
659C23#55712yes—
660C23Q8211yescharacteristic
661C23Q8212yes—
662C23#55911yescharacteristic
663C23#56011yescharacteristic
664C23#56012yes—
665C23#56011yescharacteristic
666C23H(3,𝔽4)11yescharacteristic
667C23#56212yes—
668C23#56212yes—
669C23#56212yes—
670C23#56312yes—
671C23#56311yescharacteristic
672C23#56312yes—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—24no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—82no—
772C2×C4—82no—
773C2×C4—82no—
774C2×C4—82no—
775C2×C4—82no—
776C2×C4—82no—
777C2×C4—82no—
778C2×C4—82no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4—82no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4—82no—
787C2×C4—82no—
788C2×C4—82no—
789C2×C4—82no—
790C2×C4—82no—
791C2×C4C4×C4⋊C4116yes—
792C22C2×C4×C4⋊C412yes—
793C22C42×Q811yescharacteristic
794C22#227411yescharacteristic
795C22#227512yes—
796C22#227511yescharacteristic
797C22#231512yes—
798C22#231712yes—
799C22#231812yes—
800C22#231812yes—
801C22#232112yes—
802C22#232112yes—
803C22#232212yes—
804C22#232212yes—
805C22#232912yes—
806C22#232912yes—
807C22#232911yescharacteristic
808C22#232912yes—
809C22#232912yes—
810C22#232912yes—
811C22#233012yes—
812C22#233111yescharacteristic
813C22#233311yescharacteristic
814C22#233412yes—
815C22#233512yes—
816C22#233611yescharacteristic
817C22#234512yes—
818C22#234612yes—
819C22D4×C4⋊C412yes—
820C22#234912yes—
821C22Q8×C4⋊C412yes—
822C22Q8×C4⋊C412yes—
823C22#235412yes—
824C22#235512yes—
825C22#236012yes—
826C22#236012yes—
827C22#236312yes—
828C22#236312yes—
829C22#236512yes—
830C22#236611yescharacteristic
831C22#236911yescharacteristic
832C22#236912yes—
833C22#236912yes—
834C22#237012yes—
835C22#237012yes—
836C22#237511yescharacteristic
837C22#237611yescharacteristic
838C22#237612yes—
839C22#237712yes—
840C22#237812yes—
841C22#237912yes—
842C22#238312yes—
843C22#266811yescharacteristic
844C22#267312yes—
845C22#267711yescharacteristic
846C22#268612yes—
847C22#269212yes—
848C22#269412yes—
849C22#270812yes—
850C22#271312yes—
851C22#271412yes—
852C22#272012yes—
853C22#272112yes—
854C22#273212yes—
855C22#273212yes—
856C22#273312yes—
857C22#273412yes—
858C22#277111yescharacteristic
859C22#277412yes—
860C22#277512yes—
861C22#278012yes—
862C22#278112yes—
863C22#278312yes—
864C22#278411yescharacteristic
865C22#278412yes—
866C22#278511yescharacteristic
867C22#278712yes—
868C22#278812yes—
869C22#279112yes—
870C22#279212yes—
871C22#279211yescharacteristic
872C22#280212yes—
873C22#280312yes—
874C22#280612yes—
875C22#280612yes—
876C22#280711yescharacteristic
877C22#280912yes—
878C22#281111yescharacteristic
879C4—216no—
880C4—44no—
881C4—48no—
882C4—48no—
883C4—48no—
884C4—44no—
885C4—84no—
886C4—82no—
887C4—84no—
888C2#1378212yes—
889C2#1379211yescharacteristic
890C2C4⋊C4211yescharacteristic
891C2#1381812yes—
892C2#1383111yescharacteristic
893C2#1439812yes—
894C2#1439912yes—
895C2#1440612yes—
896C2#1440712yes—
897C2#1445812yes—
898C2#1446412yes—
899C2#1446712yes—
900C2#1446812yes—
901C2#1455111yescharacteristic
902C2#1455412yes—
903C2#1456711yescharacteristic
904C2#1457012yes—
905C2#1460011yescharacteristic
906C2#1460111yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC23C22×C42
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
31. #1444C4semidirect
33. #1436C4semidirect
258. C2×C4⋊C4C4⋊C4semidirect
286. #95C42semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#14442
C2×#14362
C2×C4⋊#952
#75572
#75562
#75542